From: Freeman Dyson, Notices of the AMS, February 2009:
Birds and Frogs
Some mathematicians are birds, others are frogs. Birds
fly high in the air and survey broad vistas of mathematics out
to the far horizon. They delight in concepts that unify our thinking
and bring together diverse problems from different parts of the
landscape. Frogs live in the mud below and see only the flowers that
grow nearby. They delight in the details of particular objects,
and they solve problems one at a time. Mathematics needs both
birds and frogs. Mathematics is rich and beautiful because birds give
it broad visions and frogs give it intricate details. Mathematics is
both great art and important science, because it combines generality
of concepts with depth of structures. It is stupid to claim that
birds are better than frogs because they see farther, or that frogs
are better than birds because they see deeper. The world of mathematics
is both broad and deep, and we need birds and frogs working together to
explore it.
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